Related papers: On limit theorems for fields of martingale differe…

A central limit theorem is proved for some strictly stationary sequences of random variables that satisfy certain mixing conditions and are subjected to the "shrinking operators" $U_r(x):=[\max\{|x|-r,0\}]\cdot x/|x|,\ r \ge 0$. For…

In this work, a generalised version of the central limit theorem is proposed for nonlinear functionals of the empirical measure of i.i.d. random variables, provided that the functional satisfies some regularity assumptions for the…

We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…

The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…

Lacunary trigonometric and Walsh series satisfy limiting results that are typical for i.i.d. random variables such as the central limit theorem (Salem, Zygmund 1947), the law of the iterated logarithm (Weiss 1959) and several probability…

This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…

Let (Z n) n$\ge$0 with Z n = (Z n (i, j)) 1$\le$i,j$\le$p be a p multi-type critical branching process in random environment, and let M n be the expectation of Z n given a fixed environment. We prove theorems on convergence in distribution…

The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…

In this paper we study the functional central limit theorem for stationary Markov chains with self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n; and…

We investigate in this paper the distribution of the discrepancy of various lattice counting functions. In particular, we prove that the number of lattice points contained in certain domains defined by products of linear forms satisfies a…

We first develop a theory of conditional expectations for random variables with values in a complete metric space $M$ equipped with a contractive barycentric map $\beta$, and then give convergence theorems for martingales of…

We provide a new projective condition for a stationary real random field indexed by the lattice $\Z^d$ to be well approximated by an orthomartingale in the sense of Cairoli (1969). Ourmain result can be viewed as a multidimensional version…

In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniques and a sharp lower…

We prove functional central limit theorems for the dynamic elephant random walk in the $\sqrt{n}$ and $\sqrt{n\log n}$ orders, by applying the martingale convergence theorem and Karamata's theory of regular variation.

In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a…

We consider the existence of the integrated density of states (IDS) of the Anderson model on the Hilbert space $\ell^2(\mathbb{Z}^d)$ as analogues to the law of large numbers (LLN). In this work, we prove the analogues central limit theorem…

Using martingale convergence theorem, we prove a law of large numbers for monotone convolutions $\mu_{1}\triangleright\mu_{2}\triangleright\cdots\triangleright\mu_{n}$, where $\mu_{j}$'s are probability laws on $\mathbb{R}$ with finite…

Let $Q$ be a transition probability on a measurable space $E$ which admits an invariant probability measure, let $(X_n)_n$ be a Markov chain associated to $Q$, and let $\xi$ be a real-valued measurable function on $E$, and $S_n=\sum…

This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…

In this paper free harmonic analysis tools are used to study parabolic iteration in the complex upper half-plane. The main result here is a complete characterization for the norming constants in the monotonic central limit theorem. This…